Short Trick for Reminders on Successive Divisions

Duration: 11 min

This video lesson is available to enrolled students.

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Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: शिक्षण की अवधारणा एवं उद्देश्य / Concept and Objectives of Teaching, शिक्षण के स्तर / Levels of Teaching, शिक्षार्थी की विशेषताएँ / Learner's Characteristics, अधिगम: प्रकृति एवं सिद्धांत / Learning: Nature and Theories, संज्ञान, स्मृति एवं अधिसंज्ञान / Cognition, Memory and Metacognition, शिक्षण को प्रभावित करने वाले कारक / Factors Affecting Teaching, प्रभावी शिक्षण एवं शिक्षक / Effective Teaching and the Teacher, अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन / Instructional Objectives and Lesson Planning, शिक्षण विधियाँ / Methods of Teaching, ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ / Offline and Online Teaching Methods, शिक्षण सहायक प्रणाली / Teaching Support System, मूल्यांकन प्रणाली / Evaluation Systems, Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Teaching-Learning Aids & ICT Integration
  2. Paper - 1 | Unit - 2 | Research Aptitude: अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि / Research: Meaning, Features and Scientific Method, अनुसंधान के प्रतिमान एवं उपागम / Research Paradigms and Approaches, अनुसंधान के प्रकार / Types of Research, चर एवं मापन / Variables and Measurement, अनुसंधान की विधियाँ / Methods of Research, अनुसंधान के चरण / Steps of Research, प्रतिचयन / Sampling, आँकड़ा संग्रह के उपकरण एवं विधियाँ / Tools and Methods of Data Collection, आँकड़ा विश्लेषण एवं शोध सांख्यिकी / Data Analysis and Statistics in Research, शोध-प्रबंध एवं लेख लेखन / Thesis and Article Writing, अनुसंधान में ICT का अनुप्रयोग / Application of ICT in Research, शोध नैतिकता / Research Ethics, Introduction to Research, Validity & Reliability, Research Paradigms & Types of Research, Research Ethics, Writing & Publication
  3. Paper - 1 | Unit - 3 | Comprehension: प्रत्यक्ष बोध / Literal Comprehension, गद्यांश में शब्दावली और भाषा / Vocabulary and Language in Context, निष्कर्षात्मक बोध / Inferential Comprehension, आलोचनात्मक बोध / Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions)
  4. Paper - 1 | Unit - 4 | Communication: संचार: अर्थ, प्रकृति एवं प्रक्रिया / Communication: Meaning, Nature and Process, संचार के प्रकार एवं स्तर / Types and Levels of Communication, मौखिक एवं अमौखिक संचार / Verbal and Non-verbal Communication, संकेत विज्ञान एवं अर्थ / Semiotics and Meaning, संचार के मॉडल एवं सिद्धांत / Models and Theories of Communication, प्रभावी संचार / Effective Communication, संचार की बाधाएँ / Barriers to Communication, कक्षा संचार / Classroom Communication, जनसंचार माध्यम: प्रकार एवं विकास / Mass Media: Types and Evolution, जनसंचार एवं समाज / Mass Media and Society, डिजिटल एवं नव माध्यम / Digital and New Media, Communication Basics, Language and Semiotics, Mass Communication, Mass Media, Journalism, General Knowledge and General Studies related to Communication
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: संख्या पद्धति एवं सरलीकरण / Number System and Simplification, बीजगणित एवं आयु / Algebra and Ages, प्रतिशतता / Percentage, अनुपात, समानुपात, साझेदारी एवं मिश्रण / Ratio, Proportion, Partnership and Mixtures, औसत / Averages, लाभ, हानि एवं बट्टा / Profit, Loss and Discount, साधारण एवं चक्रवृद्धि ब्याज / Simple and Compound Interest, समय एवं कार्य / Time and Work, चाल, समय एवं दूरी / Speed, Time and Distance, क्षेत्रमिति एवं ज्यामिति / Mensuration and Geometry, क्रमचय, संचय एवं प्रायिकता / Permutation, Combination and Probability, श्रेणी / Series, कूटलेखन-कूटवाचन / Coding-Decoding, संबंध, दिशा एवं क्रम / Relationships, Directions and Ranking, व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर / Arrangements, Puzzles, Clock and Calendar, Series (Number and Letter Series) (Numerical Relations and Reasoning), Ratio and Proportion (Ratios), Powers and Exponents (Surds and Indices), Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Verbal Analogy (Word Based Analogy), Divisibility Rules, Miscellaneous, Probability
  6. Paper - 1 | Unit - 6 | Logical Reasoning: युक्ति की संरचना / Structure of Arguments, पद, परिभाषा एवं भाषा के उपयोग / Terms, Definitions and Uses of Language, निरुपाधिक प्रतिज्ञप्तियाँ / Categorical Propositions, निरुपाधिक न्यायवाक्य / Categorical Syllogism, वेन आरेख / Venn Diagrams, निगमन, आगमन एवं सादृश्यता / Deduction, Induction and Analogy, तर्कदोष / Fallacies, भारतीय तर्कशास्त्र: प्रमाण / Indian Logic: Pramanas, अनुमान एवं व्याप्ति / Anumana and Vyapti, हेत्वाभास / Hetvabhasa, Syllogisms, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Venn Diagram, School Of Thoughts, Western Logic
  7. Paper - 1 | Unit - 7 | Data Interpretation: आँकड़े एवं आलेखीय निरूपण / Data and Graphical Representation, आँकड़ा निर्वचन: तालिका / Data Interpretation: Tables
  8. Paper - 1 | Unit - 8 | Information and Communication Technology: कंप्यूटर की मूल बातें और हार्डवेयर / Computer Fundamentals and Hardware, मेमोरी, भंडारण और डेटा निरूपण / Memory, Storage and Data Representation, कंप्यूटर सॉफ्टवेयर / Computer Software, ऑफिस अनुप्रयोग / Office Applications, मल्टीमीडिया और फ़ाइल प्रारूप / Multimedia and File Formats, कंप्यूटर नेटवर्क / Computer Networks, इंटरनेट और वर्ल्ड वाइड वेब / Internet and World Wide Web, ई-मेल और ऑनलाइन संचार / Email and Online Communication, साइबर सुरक्षा / Cyber Security, डिजिटल नैतिकता, बौद्धिक संपदा और समाज / Digital Ethics, IPR and Society, क्लाउड और वितरित कंप्यूटिंग / Cloud and Distributed Computing, उभरती प्रौद्योगिकियाँ / Emerging Technologies, शिक्षा और शासन में ICT / ICT in Education and Governance, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Artificial Intelligence, Basics of COA, Introduction to OS, Introduction to CN, Data Communication, Net Layer: IP Addressing, Network Security, Number System, Number Representation, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services
  9. Paper - 1 | Unit - 9 | People Development and Environment: पारितंत्र और जैव विविधता / Ecosystems and Biodiversity, मानव और पर्यावरण की अंतःक्रिया / Human and Environment Interaction, विकास और पर्यावरण / Development and Environment, प्राकृतिक संसाधन: वन, जल और मृदा / Natural Resources – Forests, Water and Soil, ऊर्जा संसाधन / Energy Resources, वायु प्रदूषण / Air Pollution, जल प्रदूषण और उपचार / Water Pollution and Treatment, ध्वनि प्रदूषण / Noise Pollution, अपशिष्ट प्रबंधन / Waste Management, पर्यावरणीय स्वास्थ्य और विषविज्ञान / Environmental Health and Toxicology, जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ / Climate Change and Global Environmental Issues, प्राकृतिक प्रकोप और आपदा प्रबंधन / Natural Hazards and Disaster Management, भारतीय पर्यावरण कानून और नीतियाँ / Indian Environmental Laws and Policies, अंतर्राष्ट्रीय पर्यावरण समझौते / International Environmental Agreements, Ecosystem, Biomes & Environmental Issues, Noise Pollution and Waste Management, Natural Resources, Energy & Disaster Management
  10. Paper - 1 | Unit - 10 | Higher Education System: प्राचीन भारत में शिक्षा / Education in Ancient India, प्राचीन भारत के उच्च शिक्षा केंद्र / Ancient Centres of Higher Learning, औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग / Colonial Education Policies and Commissions, औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक / Colonial Colleges, Universities and Reformers, स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ / Education Commissions and Policies after Independence, राष्ट्रीय शिक्षा नीति 2020 / National Education Policy 2020, उच्च शिक्षा संस्थानों के प्रकार / Types of Higher Education Institutions, अधिगम कार्यक्रम और अकादमिक क्रेडिट / Learning Programmes and Academic Credits, व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा / Professional, Technical and Skill-Based Education, मूल्य शिक्षा और पर्यावरण शिक्षा / Value Education and Environmental Education, शासन, प्रशासन और वित्तपोषण / Governance, Administration and Financing, उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग / Regulation, Accreditation and Ranking, Jainism & Buddhism, Pre-Independence Commissions, Post-Independence Policy, Higher Education Structure & Accreditation, Universities & Learning Programmes, Types of Education & NEP 2020
  11. Live Classes: NTA UGC NET 2025 Live Class
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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on number systems, specifically focusing on the concept of remainders in division. The instructor begins by introducing the topic with a title slide and a simple example of division with a remainder, using the equation 7 ÷ 2 = 3 R1, where the remainder is highlighted. The core of the video is a problem-solving session. The first problem states that a number, when divided by 3, 4, and 7, leaves remainders of 2, 1, and 4 respectively, and asks for the remainder when the same number is divided by 84. The instructor methodically breaks down the problem using the formula: Dividend = (Divisor × Quotient) + Remainder. He sets up a table with the divisors and their corresponding remainders, then uses a step-by-step substitution method to express the original number N in terms of a variable x. He first expresses N as 3(4(7x + 4) + 1) + 2, which simplifies to N = 84x + 53. This shows that the number is of the form 84x + 53, meaning when divided by 84, the remainder is 53. The second problem involves two numbers, P and Q, with similar conditions. For P, a number is divided by 4, 5, and 7, leaving remainders 1, 4, and 1 respectively. For Q, a number is divided by 5, 6, and 8, leaving remainders 2, 3, and 4 respectively. The question asks for a possible value of P + Q. The instructor applies the same method to find that P = 140a + 53 and Q = 120b + 53. He then evaluates the given options (267, 529, 1007, 1961) by subtracting 53 from each, checking if the result is divisible by 140 and 120. He finds that 529 - 53 = 476, which is not divisible by 140, but 1007 - 53 = 954, which is not divisible by 120. He then correctly identifies that 529 - 53 = 476 is divisible by 140, and 1007 - 53 = 954 is divisible by 120, but the correct answer is 529, which is 140*3 + 53. The video concludes with a thank you message.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide that reads "NUMBER SYSTEM" in a stylized font against a gray background. This transitions to a colorful title slide with the text "NUMBER SYSTEM" and the subtitle "The mysterious world of numbers...". The slide also features the text "by YASH [KG]" and "YASH JAIN". The instructor, a man with glasses, appears in a small window in the bottom right corner. The video then moves to a new slide titled "Concept of Remainders". This slide shows a diagram of two puppies and bones, illustrating the concept of division. The equation 7 ÷ 2 = 3 R1 is written on the screen, with an arrow pointing to the 'R1' and the word "Remainder" written below it. The instructor explains that the remainder is the part that is left over after division.

  2. 2:00 – 5:00 02:00-05:00

    The video presents a problem on a slide with a yellow background. The text reads: "Q: On dividing a number successively by 3, 4 and 7, the remainder are 2, 1 and 4 respectively. If the same number is divided by 84, the remainder is __". The instructor begins to solve this problem by writing the formula for division: "Dividend = (Divisor × Quotient) + Remainder". He then sets up a table with the divisors (3, 4, 7) and their corresponding remainders (2, 1, 4). He starts by expressing the number N as N = 3q1 + 2, where q1 is the quotient. He then expresses q1 as q1 = 4q2 + 1, and q2 as q2 = 7q3 + 4. He substitutes these into the original equation to get N = 3(4(7q3 + 4) + 1) + 2.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues to simplify the expression for N. He expands the equation N = 3(4(7q3 + 4) + 1) + 2 to get N = 3(28q3 + 16 + 1) + 2, which simplifies to N = 3(28q3 + 17) + 2. Further simplification gives N = 84q3 + 51 + 2, resulting in N = 84q3 + 53. He explains that this means the number N is of the form 84x + 53, so when N is divided by 84, the remainder is 53. The video then transitions to a new problem. The slide text reads: "Q: There are two finite control units, in the first FCU, A number is successively divided 3 times by 4, 5 & 7 respectively leaving remainders as 1, 4, 1 respectively. The remainder comes out to be some value P when the same number is divided by 84. In the second FCU, some another number Q is successively divided 3 times by 5, 6 & 8 respectively leaving remainders as 2, 3, 4 respectively. Out of the given options, what could be the possible value of P + Q." The options are a) 267, b) 529, c) 1007, d) 1961. The instructor begins to solve for P by setting up the equation N = 4(5(7x + 1) + 4) + 1, which simplifies to N = 140x + 53. He then solves for Q by setting up the equation N = 5(6(8y + 4) + 3) + 2, which simplifies to N = 240y + 122. He then checks the options by subtracting 53 from each and seeing if the result is divisible by 140 and 120. He finds that 529 - 53 = 476, which is divisible by 140, and 1007 - 53 = 954, which is divisible by 120. He concludes that the correct answer is 529.

  4. 10:00 – 11:12 10:00-11:12

    The video concludes with a black screen featuring a red neon-style rectangle with the text "THANK YOU FOR WATCHING". A white lightning bolt effect runs vertically through the rectangle. The instructor's voice is heard saying "Thank you for watching". The video ends with this thank you message.

The video provides a comprehensive tutorial on solving remainder problems using a systematic, step-by-step approach. It begins with a foundational concept of remainders, illustrated with a simple example, and then progresses to more complex problems involving successive division. The core method demonstrated is the use of the division formula (Dividend = Divisor × Quotient + Remainder) to express the unknown number in terms of a variable. By substituting the conditions of successive division, the number is expressed in a form that reveals its remainder when divided by a specific number, often the least common multiple of the divisors. The video effectively applies this method to two distinct problems, one with a single unknown and another with two unknowns (P and Q), and uses the given options to verify the solution. The key takeaway is the power of algebraic substitution to solve problems that would be difficult to solve by trial and error.

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